- #1
mmh37
- 59
- 0
This is the problem
A shuttle is launched from a space station and travels away from it in a straight line. It rapidly accelerates and obtains a steady velocity of v = 4c/5 relative to the space station. The spaceship sends out radio signals of a frequency f. The spaceship is on a mission to dock with a rocket, which travels away from the Earth at velocity u. The rocket receives the shuttle's transmission at a frequency 3f/2. Show that u of the shuttle relative to the Earth is 3c/5.
GIVEN:
relativistic doppler effect; source moves towards the observer
[tex] f' = f \sqrt {\frac {c+v} {c-v}} [/tex]
velocity addition formula:
[tex] v' = \frac {v-u} {1 - v*u/c^2} [/tex]
My atempt
[tex] f' = f \sqrt {\frac {c+v} {c-v}} = 3f/2 [/tex]
hence: v = 5c/13
this is the relative speed between the shuttle and the rocket. Therefore in frame S' of the shuttle the rocket moves with a velociy u' = 5c/13
Now we have to transform to the Earth's frame of reference S, where v = 4c/5
using the velocity addition formula:
[tex] u = \frac {u' + v} {1 + v*u'/c^2} = 77/85 *c [/tex]
which is wrong.
Does anyone see why or can anyone give me a hint towards the right answer? That would be very helpful and much appreciated!
A shuttle is launched from a space station and travels away from it in a straight line. It rapidly accelerates and obtains a steady velocity of v = 4c/5 relative to the space station. The spaceship sends out radio signals of a frequency f. The spaceship is on a mission to dock with a rocket, which travels away from the Earth at velocity u. The rocket receives the shuttle's transmission at a frequency 3f/2. Show that u of the shuttle relative to the Earth is 3c/5.
GIVEN:
relativistic doppler effect; source moves towards the observer
[tex] f' = f \sqrt {\frac {c+v} {c-v}} [/tex]
velocity addition formula:
[tex] v' = \frac {v-u} {1 - v*u/c^2} [/tex]
My atempt
[tex] f' = f \sqrt {\frac {c+v} {c-v}} = 3f/2 [/tex]
hence: v = 5c/13
this is the relative speed between the shuttle and the rocket. Therefore in frame S' of the shuttle the rocket moves with a velociy u' = 5c/13
Now we have to transform to the Earth's frame of reference S, where v = 4c/5
using the velocity addition formula:
[tex] u = \frac {u' + v} {1 + v*u'/c^2} = 77/85 *c [/tex]
which is wrong.
Does anyone see why or can anyone give me a hint towards the right answer? That would be very helpful and much appreciated!
Last edited: